Simulation of temperature series and small networks from data

It is often desirable to simulate a single temperature series or a collection (network) of temperature series. Accurate simulations can enhance our understanding of temperature trends and variabilities. Simulation can also be used to generate data with known specifications, which are useful in assessing climate data processing routines such as quality control and homogenization algorithms. Possessing multiple realistic temperature series is often beneficial as only one natural record of our climate is available. The current popularity of general circulation models (GCMs) demonstrates how important simulation techniques are. However, even with sophisticated downscaling, it is difficult to replicate station temperature data that have realistic seasonal cycles as well as realistic temporal and spatial correlations. This paper reviews and studies statistical time series methods that can replicate a single series or a network of series from data. The methods are purely statistical—no atmospheric dynamics are involved—and attempt to produce replicates of the records under study. The work here develops (a) methods that simulate temperatures from a fixed season (say a particular day or month of the year) that match the distributional characteristics of the observed data; (b) methods for simulating an entire series that matches the series' temporal autocorrelations and seasonal cycle; and (c) methods for simulating a network of series that reproduce the data's observed seasonal cycles and spatial and temporal autocorrelations. Applications are given throughout, including one where a GCM series and local station data are used in tandem to describe long‐term trends and inject realistic station‐level short‐term fluctuations. This paper can be used as a tutorial for the simulation of a single climate observation, an entire climate series, or a network of multiple climate series simultaneously. Extensions of the ideas that involve GCMs are also examined. This paper shows how well‐established time series methods can be used to simulate climate temperature series and networks that match the major prominent statistical features found in temperature data. We started simple, showing how to generate a single fair draw from a fixed season, regardless of that season's statistical distribution. Thereafter, we moved to scenarios where a whole series was replicated, where several series were replicated in tandem, and where aspects of GCM‐generated data were mixed into the computat